This document serves as an introduction to logarithms, detailing key learning objectives and activities aimed at teaching exponential and logarithmic equations and their transformations. It covers definitions, properties, laws of logarithms, and techniques for solving logarithmic equations. The document emphasizes the process of rewriting equations and employing logarithmic properties to find values and simplify expressions.

1. INTRODUCTION
TO LOGARITHM
ANNALYN MANIEGO CABATINGAN

2. LEARNING OBJECTIVES
After going through this module, you
are expected to:
1. Rewrite exponential equations to
logarithmic form and vice versa
2. Distinguishes logarithmic functions,
logarithmic equations, and
logarithmic inequalities

3. Find the value of x.
ACTIVITY 1:
8)50

4. LOGARITHM
01
- is the power to which a base
must be raised to produce a
given number.
𝒃𝒄
=𝒂
log𝒃 𝒂=𝒄
Exponential form
Logarithmic form

5. SPECIAL LOGARITHMS
COMMON LOGARITHMS
are logarithms with base 10
NATURAL LOGARITHMS
are logarithms with base e

6. Rewrite the
following
exponential
equations in
logarithmic form.
ACTIVITY 2:

7. Rewrite the
following
logarithmic
equations in
exponential
form.
ACTIVITY 3:

8. A. Rewrite the following logarithmic equations in
exponential form.
ASSIGNMENT:
B. Rewrite the following exponential equations in
logarithmic form.

9. LOGARITHMIC
FUNCTIONS,
EQUATIONS,
AND
INEQUALITIES
02

10. LOGARITHMIC
EQUATION
LOGARITHMIC
INEQUALITY
LOGARITHMIC
FUNCTION
Definition An equation
involving
logarithms.
An inequality
involving
logarithms.
Function of the
form
Example

11. C. Determine whether the given is a logarithmic
function, logarithmic equation, a logarithmic
inequality or neither.
ASSIGNMENT:

12. BASIC
PROPERTIES OF
LOGARITHM
03

13. EXPLORATION:
Directions: Find the value of
the following.

14. BASIC PROPERTIES OF LOGARITHMS
Let b and x be real numbers such that
and , the basic properties of logarithms
are as follows:
• , then
¿ 𝟎
¿ 𝐱
¿ 𝐱

15. Use the basic
properties of
logarithms to
find the value of
the following
logarithmic
expressions.
ACTIVITY 1:

16. Use the basic
properties of
logarithms to
find the value of
the following
logarithmic
expressions.
SEATWORK:

17. A. Use the properties of logarithm to find
the value of the following given.
MODULAR DISTANCE LEARNING

18. A. Use the properties of logarithm to find
the value of the following given.
MODULAR DISTANCE LEARNING
2

19. LAWS OF
LOGARITHMS
04

20. EXPLORATION:
Directions: Find the value of the following.

21. LAWS OF LOGARITHMS
Let , and let .
For , , then
𝐥𝐨𝐠𝐛(𝒖𝒗)

22. EXPLORATION:
Directions: Find the value of the following.

23. LAWS OF LOGARITHMS
Let , and let .
For , , then

24. EXPLORATION:
Directions: Find the value of the following.

25. LAWS OF LOGARITHMS
Let , and let .
For , , then

26. CHANGE-OF-BASE FORMULA
Any logarithmic expression can be expressed
as quotient of two logarithmic expressions
with a common base.
Let a, b, and x be positive real numbers, with
a 1, b 1:

27. A. Use the laws of logarithms to expand the
expressions as sum, difference or multiple of
logarithms.
ASSIGNMENT:

28. B. Use the laws of logarithms to condense the
expressions as a single logarithm.
ASSIGNMENT:

29. C. Use of change-of-base formula to rewrite the
following logarithmic expressions to the
indicated bases.
ASSIGNMENT:
1) (change to base 2)
2) (change to base 5)

30. A. Use the laws of logarithms to expand the
expressions as sum, difference or multiple of
logarithms.
SEATWORK:

31. B. Use the laws of logarithms to condense the
expressions as a single logarithm.
SEATWORK:

32. C. Use of change-of-base formula to rewrite the
following logarithmic expressions to the
indicated bases.
SEATWORK:
𝐥𝐨𝐠𝟑𝟖𝟏(change to base 9)

33. SOLVING
LOGARITHMIC
EQUATIONS
05

34. TECHNIQUES:
1. Rewriting to exponential form
2. Applying the one-to-one property of
logarithmic functions
If , then .
3. Using logarithmic properties and laws
4. The Zero Factor Property:
If , then or .

35. Exercises: Solve the following
logarithmic equations.

36. Exercises: Solve the following
logarithmic equations.

37. Exercises: Solve the following
logarithmic equations.

38. ASSIGNMENT
PREPARE FOR INDIVIDUAL PERFORMANCE
TASK NEXT WEEK.
Coverage: EXPONENTIAL AND LOGARITHMIC FUCTIONS,
EQUATIONS, AND INEQUALITIES

39. If you don’t play by
the rule, don’t
complain if you
lose.